What I've seen many people do is equip the gloves of running urgently, or rocket jump, or flarejump, or sticky jump, for the only reason of letting the medic charge faster, guaranteeing a uber being ready at the start of the match.

2 Answers
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The Medic's Medi Gun now charges at an increased rate during Setup time, to remove the need for self-damage grinding

So no, damaging yourself during setup doesn't help your medic charge faster. Additionally, damaging yourself at any one time doesn't help your medic charge faster if he's using the Quickfix.

It seems obvious but worth of noting, however, that this doesn't apply on maps that lack a setup time in the first place. You do want to do "self-damage grinding" on 5CP and CTF maps, and perhaps every other single time you get out of spawn with a medic — if you've seen the pros do it, that's why.

Even in these situations, be aware that not all self-damage methods are equally helpful in making your medic heal faster. You don't have to have a flashing red HP counter to do this; the ubercharge rate reduction kicks in at 142.5% health (except during setup, apparently) and you can be overhealed up to 150%. Here's what it means:

The Gloves of Running Urgently don't damage you quite enough to keep you out of the 142.5% range. To get any advantage from that you'd have to bear with the heavy spamming 'meeediiic' until he drops below overheal, and then reap the fruits in one long shot.

One rocket jump, dealing between 27 and 46 damage, drops you between 273 and 254 — barely enough to get you and keep you below 285.

Detonator jumps are surprisingly much more effective, dealing 39–68 damage to a class that needs only 11 short of full to charge the medic faster.

That's still nothing compared to the demoman's Sticky Launcher, however: with self damage ranging between 45 and 114, you actually need to be careful about not suiciding yourself.

The scout's Boston Basher is also effective, as it is able to deal more damage faster than the regular medigun can heal. Again, make sure you don't kill yourself in the process.

Finally, the buildup rate penalty caused from your patient being healed from more than one source (medic, dispenser, cart) also applies in warmup, so be careful about that. Move away from that dispenser and overheal somebody who isn't already getting all the love.

I specifically remember that one of the earlier patches for Team Fortress 2 introduced a change where the ubercharge bar would charge faster during the round's warmup phase, making the practice you describe unnecessary.

Of course, this was a long time ago, but I doubt they've changed it back.